# Matrices

## Organizing Data with a Matrix

In the first video, we are going to organize data with a matrix.

Let’s first define matrix:
Matrix: A rectangular array of data such as numbers and symbols.

For example:

Let’s call the matrix A. Therefore:
A1,1 = 85 and
A3,2 = 86

In the second video, we are going to add and subtract data with a matrix.

To do so, we can simply either add or subtract the values in the corresponding locations in the given matrices. Note that only matrices of the same size can be added or subtracted.

For example:

And here is another one

## Multiplying a Matrix by a Scalar Number

In the third video, we are going to multiply matrix by a scalar.

We can simply multiply the scalar number by each value inside the matrix.

For example:

## Multiplying a Matrix by a Matrix

In the fourth video, we are going to multiply matrix with a matrix.

If the matrices have different sizes, multiply the corresponding numbers but of different orientations.

For example:

Since the first matrix is 2×3 and the second matrix is 3×2, your answer is a 2×2 matrix. To get the value of $A_1,1$, multiply each number of the first row in the first matrix by the corresponding number in the first column of the second matrix, and add the products (Ex:2×5+6×4+1×6). To get the value of $A_1,2$, multiply each number of the first row in the first matrix by the corresponding number in the second column of the second matrix, and add the products. To get the value of $A_2,1$, multiply each number of the secobd row in the first matrix by the corresponding number in the first column of the second matrix, and add the products.  To get the value of $A_2,2$, multiply each number of the second row in the first matrix by the corresponding number in the second column of the second matrix, and add the products.

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